That's really amazing, eyecue, thanks for the heads up. It would be a great media event to have someone request a private screening and be denied.
The TSA website says only, "Screeners are required to offer private screening to passengers who are subject to additional screening. If you are not offered private screening you have the option to request a private screening location."
Notice that TSA nowhere promises that you will get a private screening location if you request it. This stuff gets scarier and scarier the closer you look.